The impact of COVID-19 vaccines on the Case Fatality Rate: The importance of monitoring breakthrough infections

.title[
# The impact of COVID-19 vaccines on the Case Fatality Rate: The importance of monitoring breakthrough infections
]
.subtitle[
## April 9, 2022 PAA Annual Meeting
]
.author[
### Vanessa di Lego1 Miguel Sánchez-Romero 1 2 Alexia Prskawetz1 2 3
]
.institute[
### 1 Wittgenstein Centre (IIASA, OeAW, University of Vienna) Vienna Institute of Demography at the Austrian Academy of Sciences 2 International Institute for Applied Systems Analysis, Laxenburg, Austria 3 Institute of Statistics and Mathematical Methods in Economics, Research Unit Economics, TU Wien
]

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# Motivation

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Fig. 1 Case Fatality Rate (CFR) and %Fully Vaccinated Trajectories
 
 <div class="container">
 <img class="under" src="data:image/png;base64,#C:/Users/vdile/Documents/Git/CFR_present/img/vax_change.gif"/> 
 <img class="over" src="data:image/png;base64,#C:/Users/vdile/Documents/Git/CFR_present/img/cfr_change.gif"/> 
 </div>
 
.remark-slide-content3[Source: Our World in Data (Mathieu et al. 2021)]

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Fig. 1 Case Fatality Rate (CFR) and %Fully Vaccinated Trajectories
 
<img src="data:image/png;base64,#img/cfr_all_paa.png" width="95%" style="display: block; margin: auto;" />

Fig. 2 Panel (A) %Case-Fatality Rate (CFR); Panel (B) Share of fully vaccinated persons (%). Austria, by age, from Jan to Dec 2021

<img src="data:image/png;base64,#img/fig2.png" width="95%" style="display: block; margin: auto;" />
.remark-slide-content3[Source: The number of people vaccinated at each group is taken from BMSGPK, Österreichisches COVID-19 Open Data Informationsportal (2021)]

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# What is driving this pattern in the CFR?
 ## Are vaccines not being effective in reducing deaths?

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# The Sensitivity of the Case-Fatality Rate (CFR) as an Indicator

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class:remark-slide-content

## The CFR is particularly sensitive to 1:

- demographic factors

- delays in reported cases

- testing policies

]

`$${CFR}_{t,a}=\frac{\text{Deaths}_{t,a}}{\text{Reported Cases}_{t,a}}$$`

#### .red[Any] factor that impacts the number of .red[confirmed deaths] from a disease and the number of .red[reported cases] in a given time ###
 
]]

.footnote[[1] (Dowd et al. 2020; Rajgor et al. 2020; Goldstein and Lee 2020; Green et al. 2020; Harman et al. 2021; Smith 2021; Luo et al. 2021; Undurraga et al. 2021)]

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# The CFR in the presence of Vaccines

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.content-box-blue[
`$${CFR}_{t,a}=\frac{\mathcal{D}^{U}_{t,a}+\mathcal{D}^{V}_{t,a}}{d^{U}_{t,a}\mathcal{I}^{U}_{t,a}+\color{red}{d^{V}_{t,a}\mathcal{I}^{V}_{t,a}}}$$`
]

.content-box-blue[
`$$\text{CFR}_{t,a}=\text{CFR}^{U}_{t,a}(1-\color{red}{\gamma_{t,a}})+\text{CFR}^{V}_{t,a}\color{red}{\gamma_{t,a}}$$`]

`$\text{CFR}_{t,a}$` being the weighted sum of `$\text{CFR}^{U}_{t,a}$` and `$\text{CFR}^{V}_{t,a}$` with weights `$\color{red}{\gamma_{t,a}}$`:

.pull-left-1[.content-box-red[
`$$\gamma_{t,a}= \frac{\color{red}{d^{V}_{t,a}\mathcal{I}^{V}_{t,a}}}{{d^{U}_{t,a}\mathcal{I}^{U}_{t,a}+\color{red}{d^{V}_{t,a}\mathcal{I}^{V}_{t,a}}}}$$`]]

.pull-right-2[ 
the ratio between the total number of COVID vaccine .red[breakthroughs] and the total number of COVID-associated ever infected and detected cases]

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.content-box-blue[
`$$\text{CFR}_{t,a}=\text{CFR}^{U}_{t,a}(1-\color{red}{\gamma_{t,a}})+\text{CFR}^{V}_{t,a}\color{red}{\gamma_{t,a}}$$`]

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.pull-left-2[.content-box-blue[
`$$\text{CFR}^{V}_{t,a}=\text{CFR}^{U}_{t,a}\frac{(1-\color{red}{\beta_{a}})}{\color{red}{Z_{t,a}}}$$`]]

`$Z_{t,a}$` = ratio of detection rates between the vaccinated and the unvaccinated

if `$Z_{t,a}=1$`, the rate of detection among vaccinated and unvaccinated is the same]

.pull-left-2[.content-box-red[
`$$(1 − \beta_{a} ) = Z_{t,a}$$`
the CFR will remain
**unchanged**, regardless the fact that the case fatality rate of the vaccinated is
**lower** than the case fatality rate of the unvaccinated. ]]

.pull-left-2[.content-box-purple[the **lower** `$\beta_{a}$`, the **higher** `$Z_{t,a}$` to keep CFR **constant**. the **higher** `$\beta_{a}$`, the **lower** `$Z_{t,a}$` to keep CFR constant
 ]]

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We illustrate the effect CFR scenarios that result from a different combination of `$\beta_{a}$` and `$Z_{t,a}$` values.

- Focus on the 84+, that has the highest risk of dying and was the first vaccinated.

- Use Austria as case study for which we have detailed data on deaths, infections, vaccination status and testing by age; Consistent and unique testing policy.

- vaccine effectiveness in reducing deaths for ages above 84 is set at 0.853

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# Results

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.remark-slide-content2[Figure 3. Evolution of the %CFR for the age group 84+ in Austria (Jan-Dec 2021) by three different parameter values of]   `$\beta_{(84+)}$` .remark-slide-content2[and] `$Z_{(t,84+)}$`

<img src="data:image/png;base64,#img/sim_adj.png" width="90%" style="display: block; margin: auto;" />
.remark-slide-content3[Source: Simulated CFR values are calculated using data from (Richter et al. 2020b, a)and BMSGPK, COVID-19 Open Data Informationsportal (2021)]

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# Discussion

- CFR decline may **not** imply that vaccines are being effective in reducing deaths
--

- A constant CFR can **still** mean that vaccines are effective in reducing deaths
--

- Detecting infections among both the vaccinated and unvaccinated population is key
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## Take-away: unless vaccinated people are **also** tested, it is hard to use the CFR as an indicator for monitoring the pandemic

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Fig. 4 Financial Times Graph on the CFR in Hong Kong: What is the CFR telling us?

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Thank you!